Daryl Murphy grabbed the all-important goal in the 76th minute with his fourth goal of the season just when it seemed as though the well-matched teams would have to settle for a share of the spoils.
Manager Roy Keane called for patience and more consistency if the Black Cats are to climb their way into the promotion frame and, although they enjoyed long spells of possession, the improvement is slow in forthcoming.
Sunderland's early dominance was let down by casual and wayward passing, especially when bringing the ball out of defence much to the frustration of the home fans.
When Murphy tested goalkeeper Lee Camp with a low drive when cutting in from the right, the Black Cats looked capable of continuing their recent good form.
But sadly they were completely out of touch with the Canaries rarely under pressure, causing problems at times with lively breaks led by Darren Huckerby.
Murphy was unable to get on the end of a teasing centre from Ross Wallace when well-placed at the far post, but the home side almost took the lead in the 23rd minute.
Grant Leadbitter was impeded on the left and, from Graham Kavanagh's free-kick, Steve Caldwell's powerful header was brilliantly saved by Camp diving to his left.
The ball was scrambled behind and, from the corner, Wallace fired wide.
A shot on the turn from Elliott relieved the boredom and then the Republic of Ireland international linked up with Murphy before shooting across the face of goal.
Norwich's leading scorer Robert Earnshaw latched on to a mistake by Kavanagh only to lob the ball over the bar with goalkeeper Darren Ward off his line.
Twice within the space of a minute Sunderland came close to making the breakthrough. Murphy cut in along the byline after linking up with Elliott only to shoot into the side-netting with colleagues up in support. Elliott then took advantage of hesitancy in the Canaries defence only to shoot wide.
Norwich looked hopefully for a penalty on the hour when Elliott challenged Huckerby from behind but referee Phil Joslin, who helped contribute to the dreadful proceedings with his constant whistle blowing, showed no interest.
Leadbitter was just too high and Wallace fired over the bar but, seconds after Darren Ward had reacted smartly to deny Earnshaw, Sunderland went ahead.
Dwight Yorke, who had replaced Leadbitter two minutes earlier, found a subdued Murphy, but the lone striker turned smartly to beat Camp with a crisp drive.
Huckerby missed a great chance to haul Norwich back on level terms in the 82nd minute when he went clear from what looked an offside position only to be eventually crowded out.
Sunderland held on for a third win in five matches and climb into their highest position of the season.